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AGRICULTURE 


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UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.  282 


THE  ENERGY  VALUE  OF  MILK  AS 
RELATED  TO  COMPOSITION 

Formulas  for  the  Computation  of  the  Energy 

BY  0.  R.  OVERMAN  AND  F.  P.  SANMANN 


URBANA,  ILLINOIS,  DECEMBER,  1926 


CONTENTS 

PAGES 

EXPERIMENTAL  PART 207-208 

STATISTICAL  PART 212-214 

APPLICATION 215-218 

CONCLUSIONS 218 

LITERATURE  CITED. .  .  .218-219 


THE  ENERGY  VALUE  OF  MILK  AS 
RELATED  TO  COMPOSITION 

Formulas  for  the  Computation  of  the  Energy 

BY  O.  R.  OVERMAN,  Assistant  Chief  in  Dairy  Chemistry,  and 
F.  P.  SANMANN,  Associate  in  Dairy  Manufactures 

A  knowledge  of  the  energy  valuea  of  milk  or  the  number  of  calories 
of  heat  which  can  be  produced  by  the  complete  combustion  of  a  given 
quantity  of  milk  is  of  interest  and  value  both  to  students  of  human 
nutrition  and  to  those  of  animal  nutrition.  Formulas  have  been  devel- 
oped for  the  computation  of  this  value.  Gaines  and  Davidson,1  work- 
ing from  data  compiled  by  Stocking  and  Brew,2  have  derived  the  form- 
ula E  =  49.64  (2.66  +  i),  in  which  E  is  the  energy  of  milk  solids  and 
t  is  the  percentage  of  fat.  This  formula,  which  gives  the  energy  value 
per  pound  of  milk,  is  based  on  average  analyses,  and  was  used  in  esti- 
mating the  energy  yield  of  cows.  Frederiksen3  reports  that  Director 
A.  C.  Andersen  gives  the  heat  of  combustion  of  milk  to  be  equal  to 
(percentage  of  fat  X  113.5)  +  290  calories  per  kilogram. 

The  present  investigation  was  begun  for  the  purpose  of  determining 
the  energy  values  of  milks  of  different  composition,  and  of  comparing 
such  determined  values  with  corresponding  energy  values  as  computed 
from  the  composition  of  the  milk.  As  the  work  progressed,  the  possi- 
bility of  applying  statistical  methods  to  these  results,  for  the  purpose 
of  deriving  formulas  by  which  the  energy  value  of  milk  might  be 
computed  from  its  composition,  was  recognized.  This  treatment  of 
the  data  resulted  in  the  derivation  of  formulas  based,  first,  upon  the 
complete  analysis  of  the  milk;  second,  on  the  fat,  protein,  and  lactose 
content;  and  third,  on  the  fat  alone.  The  details  of  the  statistical 
methods  by  which  these  formulas  were  derived,  and  a  discussion  of 
the  application  of  the  formulas,  are  presented  in  the  following  pages. 

EXPERIMENTAL  PART 

The  milks  studied  were  obtained  from  the  purebred  and  experi- 
mental herds  of  the  Dairy  Department  of  the  University  of  Illinois. 


"Where  the  terms  energy  value  or  calorie  are  used  it  is  to  be  understood  that  the 
large  calorie  is  the  unit  of  heat  involved. 

207 


208  BULLETIN  No.  282  [December, 

The  samples  represent  milk  from  Ayrshire,  Guernsey,  Holstein,  and 
Jersey  cows,  and  from  cows  in  the  Guernsey-Holstein  crossbred  experi- 
mental herd.  At  the  beginning  of  the  work  a  few  samples  were  taken 
from  single  milkings  of  individual  cows.  Later,  each  sample  was  a  com- 
posite made  from  all  the  milk  produced  by  one  cow  during  three  days. 
Samples  were  taken  at  all  stages  during  the  normal  lactation  periods  of 
the  cows. 

The  samples  were  preserved  with  formaldehyde,  added  in  ap- 
proximately the  proportions  recommended  by  Palmer,4  and  were  kept 
in  half-gallon  glass  fruit  jars  fitted  with  glass  lids  and  rubber  rings. 

Determinations  of  percentages  of  fat,  total  protein,  lactose,  and 
total  solids,  and  for  specific  gravity  and  energy  value,  were  made  for  all 
samples  studied. 

The  specific  gravity  was  determined  with  a  specific-gravity  balance 
of  the  chainomatic  type.  The  percentage  of  fat  was  determined  by  the 
Roese-Gottlieb  method,  using  about  5  grams  of  the  sample. 

Total  protein  was  determined  by  the  Official  Kjeldahl  method. 
Lactose  was  determined  by  the  Official  Optical  method,  mercuric  nitrate 
being  used  as  the  precipitant.  A  Schmidt-Haensch  saccharimeter  was 
used  for  all  polarizations. 

Total  solids  were  determined  by  the  Official  method.  A  Parr  adiabatic 
oxygen-bomb  calorimeter  was  used  for  all  determinations  of  energy 
value.  The  water  equivalent  of  the  calorimeter  was  carefully  determined 
by  several  combustions  of  weighed  quantities  of  pure  benzoic  acid. 

About  10  grams  of  the  milk  sample  were  accurately  weighed  into 
an  Illium  combustion  capsule  and  dried  on  a  water  bath.  The  dried 
samples  were  kept  in  a  desiccator  until  the  combustion  could  be  made. 
Combustions  were  made  in  oxygen  under  a  pressure  of  25  to  30  atmos- 
pheres. Temperature  changes  were  read  to  thousandths  of  a  degree 
centigrade  on  a  standardized  Beckmann  thermometer.  The  rise  in 
temperature  was  corrected  in  every  case  for  stem  emergence  and  for  the 
setting  of  the  Beckmann  thermometer.  The  total  energy  change  in  the 
combustion  was  then  computed  by  multiplying  the  rise  in  temperature  in 
degrees  by  the  water  equivalent  of  the  calorimeter.  This  value  was  then 
corrected  for  the  heat  liberated  by  the  combustion  of  the  iron  fuse  wire 
and  the  heat  liberated  in  the  formation  of  nitric  acid  during  the  com- 
bustion. A  total  of  212  samples  of  milk  were  so  studied. 

All  analytical  results  are  tabulated  in  the  first  six  columns  of  Table  1, 
arranged  down  the  column  in  the  order  of  increasing  fat  percentages. 
These  results  in  each  case  are  the  means  of  closely  corresponding 
duplicate  determinations. 


1926} 


THE  ENERGY  VALUE  OF  MILK 


209 


TABLE  1. — ANALYSES  OF  212  MILK  SAMPLES  WITH  COMPUTED  AND  DETERMINED 
ENERGY  VALUES 


Calories  per  quart 

Fat 

Pro- 

Lactose 

Total 

solids 

Specific 

Computed 

gravi  y 

Deter- 
mined 

Meta- 

Form- 

Form- 

Form- 

Form- 

Total 

boliz- 

ula 

ula 

ula 

ula 

A 

B 

C 

D 

E 

F 

able 

1 

2 

3 

4 

perct. 

perct. 

perct. 

perct. 

cals. 

cals. 

2.68 

2.93 

4.72 

10.96 

1.0298 

580.4 

585.8 

533.3 

582.2 

582.4 

536.8 

583.6 

2.72 

3.27 

3.92 

10.58 

1.0291 

565.8 

577.1 

518.5 

577.7 

586.9 

541.0 

584.3 

2.76 

2.86 

4.89 

11.13 

1.0310 

589.2 

596.3 

544.8 

591.3 

591.5 

545.2 

591.6 

2.82 

2.72 

5.05 

11.07 

1.0312 

585.3 

600.3 

541.2 

589.5 

598.3 

551.5 

593.7 

2.85 

2.91 

4.81 

11.04 

1.0317 

591.1 

604.6 

551.9 

593.7 

601.7 

554.7 

600.3 

2.86 

2.66 

4.78 

11.18 

1.0301 

592.0 

589.5 

541.0 

595.5 

602.8 

555.8 

586.9 

2.94 

3.10 

4.60 

11.48 

1.0319 

618.9 

615.3 

559.2 

618.8 

611.9 

564.2 

613.2 

2.94 

3.18 

4.82 

11.55 

1  .  0329 

622.6 

628.8 

571.4 

622.3 

611.9 

564.2 

623.4 

2.94 

2.92 

4.46 

11.10 

1.0310 

607.3 

599.4 

.546.2 

601.8 

611.9 

564.2 

599.7 

2.94 

3.03 

4.80 

11.20 

1.0306 

602.9 

618.4 

563.5 

606.5 

611.9 

564.2 

614.8 

2.96 

3.06 

4.70 

11.15 

1.0316 

604.8 

618.6 

563.1 

606.5 

614.2 

566.3 

615.5 

2.98 

2.88 

4.48 

11.09 

1.0316 

603.0 

601.9 

549.3 

602.9 

616.5 

568.4 

601.7 

2.98 

3.02 

4.84 

11.37 

1.0321 

606.6 

623.8 

569.1 

614.8 

616.5 

568.4 

618.9 

2.99 

2.82 

4.71 

11.08 

1.0310 

595.0 

607.9 

556.4 

601.4 

617.6 

569.4 

605.5 

2.99 

2.94 

4.62 

11.25 

1.0313 

606.2 

611.3 

557.8 

610.1 

617.6 

569.4 

609.6 

3.01 

2.97 

5.16 

11.71 

1.0318 

625.2 

635.9 

582.1 

627.6 

619.9 

571.6 

627.5 

3.02 

2.97 

4.75 

11.48 

1.0319 

623.8 

621.1 

567.0 

620.5 

621.0 

572.6 

617.4 

3.04 

3.13 

4.84 

11.56 

1.0317 

614.0 

635.1 

578.4 

627.0 

623.3 

574.7 

630.3 

3.04 

3.16 

5.01 

11.90 

1.0325 

638.1 

644.0 

586.7 

639.9 

623.3 

574.7 

636.5 

3.04 

3.18 

4.92 

11.76 

1.0326 

639.0 

641.5 

585.7 

635.2 

623.3 

574.7 

635.2 

3.06 

3.15 

5.11 

12.23 

1  .  0353 

659.7 

650.7 

593.5 

653.2 

625.6 

576.8 

640.4 

3.08 

2.87 

5.21 

11.68 

1.0318 

624.4 

638.6 

586.3 

628.4 

627.9 

578.9 

629.7 

3.09 

2.91 

4.96 

11.66 

1  .  0324 

630.9 

632.4 

579.3 

629.5 

629.0 

580.0 

626.1 

3.10 

2.92 

5.03 

11.50 

1  .  0308 

621.4 

635.5 

582.4 

623.9 

630.1 

581.0 

629.4 

3.10 

3.00 

4.96 

11.88 

1.0325 

643.4 

638.4 

583.7 

639.8 

630.1 

581.0 

631.9 

3.12 

2.88 

5.10 

11.79 

1.0321 

653.7 

638.9 

586.0 

635.1 

632.4 

583.1 

631.0 

3.12 

3.12 

4.93 

11.70 

1.0333 

634.4 

646.3 

589.5 

636.2 

632.4 

583.1 

639.4 

3.14 

2.90 

4.75 

11.49 

1.0316 

633.0 

627.7 

574.6 

626.1 

634.7 

585.2 

624.5 

3.14 

2.91 

4.64 

11.39 

1.0314 

631.1 

624.0 

570.6 

622.7 

634.7 

585.2 

622.1 

3.16 

2.98 

5.08 

11.56 

1.0312 

623.8 

646.5 

592.2 

630.2 

637.0 

587.3 

639.5 

3.17 

3.11 

4.48 

11.72 

1.0313 

635.8 

631.6 

574.8 

640.5 

638.1 

588.4 

631.4 

3.18 

2.89 

4.85 

11.55 

1  .  0298 

628.6 

633.6 

580.6 

629.9 

639.2 

589.4 

630.3 

3.18 

3.03 

5.02 

11.82 

1.0312 

634.2 

648.8 

593.5 

642.1 

639.2 

589.4 

642.4 

3.18 

3.11 

4.88 

11.74 

1  .  0329 

637.4 

649.0 

592.2 

640.8 

639.2 

589.  4 

643.0 

3.19 

3.05 

4.74 

11.63 

1  .  0302 

632.8 

639.4 

583.7 

636.4 

640.4 

590.5 

636.9 

3.20 

2.88 

4.84 

11.42 

1  .  0294 

625.1 

634.2 

581.4 

625.9 

641.5 

591.6 

631.3 

3.20 

3.26 

4.78 

11.80 

1  .  0327 

644.7 

655.1 

595.8 

646.9 

641.5 

591.6 

650.3 

3.22 

3.00 

4.74 

11.77 

1.0313 

638.7 

641.9 

587.0 

642.4 

643.8 

593.7 

636.9 

3.22 

3.18 

4.48 

11.70 

1.0315 

651.3 

639.4 

582.0 

643.6 

643.8 

593.7 

639.7 

3.25 

2.83 

5.18 

11.96 

1.0317 

646.3 

650.5 

598.4 

647.4 

647.2 

596.8 

642.2 

3.29 

3.00 

4.94 

11.94 

1.0310 

647.4 

653.8 

598.8 

652.1 

651.7 

601.0 

648.6 

3.32 

3.09 

5.17 

12.30 

1.0323 

667.8 

671.2 

614.7 

668.2 

655.1 

604.2 

662.4 

3.35 

2.88 

5.26 

12.01 

1.0319 

652.1 

665.4 

612.4 

655.1 

658.6 

607.3 

656.1 

3.37 

3.20 

5.03 

12.14 

1.0317 

671.3 

676.1 

617  6 

667.0 

660.8 

609.5 

669.1 

3.39 

3.07 

4.69 

11.68 

1.0315 

652.8 

657.4 

600.8 

649.4 

663.1 

611.6 

654.8 

3.41 

2.90 

5.24 

12.17 

1  .  0329 

669.6 

671.8 

61S.3 

664.8 

665.4 

613.7 

662.1 

3.42 

3.11 

4.94 

11.90 

1  .  0322 

670.0 

672.5 

615.2 

659.3 

666.5 

614.7 

666.4 

3.42 

3.38 

4.83 

12.34 

1.0316 

682.7 

682.8 

621.1 

680.7 

666  5 

614.7 

678.1 

3.43 

3.13 

5.27 

12.64 

1  .  0327 

693.1 

687.5 

630.1 

687.3 

667.7 

615.8 

C77.2 

3.45 

3.06 

4.58 

11.66 

1.0314 

653.3 

658.0 

601.4 

652.0 

670.0 

617.9 

656.7 

3.46 

3.14 

5.15 

12.24 

1.0318 

679.9 

685.6 

627.9 

674.2 

671.1 

618.9 

677.2 

3.47 

3.48 

4.77 

12.37 

1  .  0322 

684.1 

691.0 

627.4 

686.3 

672.2 

620.0 

686.4 

3.49 

3.02 

4.98 

12.32 

.0322 

678.1 

675.3 

619.4 

677.3 

674.5 

622.1 

668.9 

3.50 

3.10 

4.87 

12.04 

.0310 

671.7 

675.6 

618.4 

668.8 

675.6 

623.1 

671.2 

3.50 

3.64 

5.26 

12.87 

.0351 

704.0 

723.6 

657.3 

708.2 

675.6 

623.1 

710.9 

3.51 

2.98 

5.14 

12.26 

.0319 

676.3 

680.8 

635.4 

675.0 

676.8 

624.2 

672.8 

3.52 

2.90 

5.26 

12.22 

.0320 

670.1 

682.0 

628.2 

672.4 

677.9 

625  2 

672.6 

3.52 

3.01 

4.86 

12.10 

.0333 

676.1 

673.5 

617.6 

670.8 

677.9 

625.2 

667.9 

3.52 

3.12 

4.90 

12.10 

.0322 

673.0 

680.5 

622.8 

672.5 

677.9 

625.2 

674.9 

3.56 

2.94 

5.21 

12.20 

.0312 

676.3 

685.4 

630.8 

674.5 

682.4 

629.5 

677.0 

3.56 

3.55 

5.16 

12.97 

.0338 

703.4 

719.2 

654.3 

713.9 

682.4 

629.5 

708.8 

3.58 

3.22 

5.14 

12.58 

.0325 

694.4 

700.9 

641.6 

694.8 

684.7 

631.6 

692.2 

3.59 

3.10 

5.39 

12.72 

1  .  0326 

703.4 

704.9 

647  6 

698.0 

685.9 

632.6 

693.3 

3.60 

3.05 

4.82 

12.24 

1.0308 

677.8 

679.7 

623.2 

681  0 

687.0 

633.7 

676.2 

3.60 

3.08 

5.05 

12.16 

1.0310 

678.4 

690.4 

633.4 

677.8 

687.0 

633.7 

684.0 

3.60 

3.52 

4.73 

12.57 

1.0331 

698.3 

704.0 

639.4 

701.5 

687.0 

633.7 

699.3 

3.61 

3.12 

5.31 

12.66 

1  .  0322 

697.2 

704.4 

646.8 

697.3 

688.1 

634.7 

694.0 

210 


BULLETIN  No.  282 


[December, 


TABLE  1. — ANALYSES  OF  212  MILK  SAMPLES  WITH  COMPUTED  AND  DETERMINED 
ENERGY  VALUES — (Continued) 


Calories  per  quart 

Fat 

Pro- 

Lactose 

Total 

Specific 

Computed 

VG1D 

SOllGS 

gravity 

Deter- 
mined 

Meta- 

Form- 

Form- 

Form- 

Form- 

Total 

boliz- 

ula 

ula 

ula 

ula 

A 

B 

C 

D 

E 

F 

able 

1 

2 

3 

4 

perct. 

perct. 

•perct. 

perct. 

cals. 

cals. 

3.62 

2.93 

5.10 

12.18 

1  .  0324 

692.8 

686.7 

632.1 

677.1 

689.3 

635.8 

679.0 

3.62 

3.25 

5.24 

12.51 

1  .  0325 

696.3 

710.1 

650.2 

694.5 

689.3 

635.8 

700.1 

3.64 

3.06 

4.50 

12.06 

1  .  0308 

675.6 

671.5 

614.8 

677.3 

691.5 

637.9 

671.8 

3.64 

3.14 

4.83 

12.10 

1  .  0333 

674.4 

690.5 

632.1 

679.4 

691.5 

637.  S 

685.0 

3.64 

3.62 

5.16 

12.84 

1.0348 

708.6 

731.0 

664.7 

714.4 

691.5 

637.9 

719.9 

3.68 

3.08 

4.56 

11.85 

1.0313 

649.1 

679.0 

621.5 

671.7 

696.1 

642.1 

678.1 

3.70 

3.00 

4.99 

12.16 

1.0329 

684.1 

694.0 

637.9 

682.0 

698.4 

644.2 

687.1 

3.70 

3.50 

4.81 

12.77 

1  .  0322 

711.9 

714.5 

650.0 

713.8 

698.4 

644.2 

709.4 

3.71 

2.84 

5.34 

12.33 

1  .  0328 

689.6 

699.3 

646.2 

685.4 

699.5 

645.3 

688.7 

3.71 

3.23 

4.79 

12.48 

1  .  0328 

699.8 

699.9 

639.9 

699.0 

699.5 

645.3 

695.2 

3.72 

3.08 

4.85 

12.29 

1.0317 

681.9 

694.6 

636.6 

689.7 

700.6 

646.3 

689.5 

3.72 

3.11 

5.02 

12.36 

1.03H 

693.6 

702.0 

644.2 

692.9 

700.6 

646.3 

695.7 

3.75 

3.17 

4.99 

12.38 

1  .  0308 

695.5 

706  .  5 

647.6 

695.7 

704.1 

649.5 

700.9 

3.77 

2.99 

4.95 

12.40 

1.0324 

700.8 

697.8 

641.8 

694.8 

706.3 

651.6 

691.8 

3.78 

3.10 

4.50 

12.12 

1.0310 

683.1 

686.6 

628.5 

687.7 

707.5 

652.6 

686.7 

3.80 

3.15 

4.76 

12.32 

1  .  0329 

693.9 

702.4 

643.6 

696.5 

709.7 

654.7 

698.2 

3.82 

2.79 

5.02 

12.20 

1.0331 

681.8 

694.4 

641.6 

686.4 

712.0 

656.8 

687.4 

3.86 

3.02 

4.50 

12.28 

1.0311 

691.8 

689.4 

632.5 

696.6 

716.6 

661.0 

689.6 

3.86 

3.36 

5.41 

13.21 

1  .  0338 

731.5 

745.3 

683.1 

735.0 

716.6 

661.0 

732.4 

3.89 

3.42 

4.74 

12.70 

1.0314 

718.2 

723.9 

660.3 

720.0 

720.0 

664.2 

720.4 

3.89 

3.64 

5.07 

13.06 

1.0336 

738.9 

750.4 

683.2 

736.5 

720.0 

664.2 

741.2 

3.91 

3.43 

5.24 

13.23 

1  .  0332 

739.5 

746.7 

683.2 

740.0 

722.3 

666.3 

736.2 

3.92 

2.99 

4.42 

12.24 

1  .  0308 

694.6 

689.8 

633.3 

698.0 

723.4 

667.4 

691.3 

3.93 

3.14 

5.16 

12.96 

1.0342 

724.5 

730.0 

671.1 

726.4 

724.5 

668.4 

720.1 

3  94 

3.37 

5.02 

12.78 

1  .  0329 

718.2 

737.4 

674.7 

724.2 

725.7 

669.5 

729.8 

3.96 

3.47 

4.01 

12.24 

1.0314 

698.4 

704.7 

639.9 

709.1 

727.9 

671.6 

710.0 

3.97 

3.71 

5.15 

13.36 

1.0351 

754.8 

765.7 

697.2 

753.1 

729.1 

672.6 

754.4 

3.98 

3.00 

4.88 

12.36 

1.0313 

706.4 

713.8 

657.2 

704.6 

730.0 

673.7 

709.6 

3.98 

3.16 

4.88 

12.49 

1.0331 

708.1 

724.1 

664.6 

712.3 

730.0 

673.7 

718.2 

3.99 

3.57 

4.58 

12.83 

1.0314 

727.4 

735.0 

668.7 

733.1 

731.4 

674.7 

733.4 

4.02 

3.29 

5.22 

13.26 

1.0339 

745.5 

748.6* 

687.1 

744.8 

734.8 

677.9 

738.0 

4.02 

3.66 

4.50 

12.84 

1.0318 

723.7 

740.0 

672.0 

736.8 

734.8 

677.9 

738.8 

4.04 

3.62 

5.44 

13.54 

1.0355 

760.1 

778.6 

711.5 

761.3 

737.0 

680.0 

763.6 

4.05 

3.41 

5.12 

13.26 

1.0328 

751.4 

753.4 

689.8 

748.5 

738.2 

681.0 

744.6 

4.07 

4.32 

4.98 

13.97 

1  .  0365 

790.5 

803.4 

724.2 

792.0 

740.4 

683.2 

792.0 

4.08 

3.34 

5.17 

13.17 

1.0319 

743.9 

753.4 

691.0 

745.4 

741.6 

684.2 

744.8 

4.09 

3.05 

5.17 

12.84 

1  .  0306 

725.0 

737.2 

679.7 

728.6 

742.7 

685.3 

730.0 

4.10 

3.74 

4.71 

13.06 

1  .  0308 

749.4 

758.9 

689.7 

750.1 

743.9 

686.3 

756.1 

4.12 

3.41 

3.96 

12.14 

1.0306 

711.0 

713.3 

649.2 

712.9 

746.1 

688.4 

719.9 

4.13 

3.16 

5.18 

12.95 

1.0330 

738.6 

749.0 

689.5 

736.8 

747.3 

689.5 

739.9 

4.16 

3.06 

5.01 

12.84 

1.0312 

726.7 

738.4 

680.4 

732.9 

750.7 

692.6 

732.6 

4.16 

3.34 

4.84 

12.99 

1.0317 

748.6 

747.8 

685.0 

743.7 

750.7 

692.6 

743.3 

4.16 

3.36 

5.36 

13.42 

1.0336 

757.4 

770.3 

707.4 

759.0 

750.7 

692.6 

758.2 

4.17 

3.67 

5.07 

13.36 

1.0335 

765.9 

777.3 

709.0 

763.1 

751.8 

693.7 

768.2 

4.18 

3.70 

4.76 

13.47 

1.0322 

773.0 

766.9 

699.0 

769.1 

753.0 

694.7 

762.5 

4.20 

3.21 

5.07 

13.30 

1  .  0332 

753.4 

754.1 

693.4 

754.8 

755.2 

696.8 

746.0 

4.25 

3.62 

5.46 

13.80 

1.0341 

792.1 

797.2 

729.8 

782.1 

760.9 

702.1 

783.2 

4.28 

3.71 

4.99 

13.66 

1.0341 

782.0 

786.8 

717.5 

781.2 

764.3 

705.3 

778.2 

4.32 

3.39 

4.68 

13.19 

1  .  0328 

743.7 

759.6 

695.5 

761.0 

768.9 

709.5 

756.2 

4.32 

4.08 

4.81 

13  96 

1  .  0338 

799.9 

803.9 

728.3 

801.2 

768.9 

709.5 

797.1 

4.38 

3.14 

4.94 

12.92 

1.0328 

748.4 

761.1 

701.2 

749.1 

775.7 

715.8 

755.0 

4.38 

3.76 

4.91 

13.70 

1  .  0327 

792.6 

794.5 

724.2 

788.9 

775.7 

715.8 

787.9 

4.39 

3.71 

5.41 

14.06 

1.0350 

803.4 

813.7 

743.1 

801.0 

776.8 

716.8 

799.4 

4.41 

3.22 

5.18 

13.35 

1.0325 

762.8 

777.3 

716.1 

767.7 

779.1 

719.0 

768.5 

4.41 

3.68 

5.10 

13.91 

1  .  0334 

797.0 

800.6 

731.6 

796.7 

779.1 

719.0 

791.3 

4.42 

3.24 

5.29 

13.55 

1  .  0324 

779.7 

783.5 

722.0 

775.8 

780.3 

720.0 

773.4 

4.42 

3.29 

5.01 

13.31 

1.0311 

768.7 

774.5 

712.1 

768.2 

780.3 

720.0 

768.7 

4.45 

3.72 

4.78 

13.74 

1  .  0326 

794.8 

793.5 

723.6 

793.8 

783.7 

723.2 

788.6 

4.46 

3.36 

4.86 

13.32 

1.0312 

760.8 

776.3 

712.6 

772.3 

784.8 

724.2 

772.1 

4.46 

3.50 

5.06 

13.78 

1.0338 

792.7 

793.8 

727.7 

791.6 

784.8 

724.2 

785.0 

4.47 

3.94 

4.77 

13.90 

1  0328 

807.3 

807.3 

733.7 

804.6 

785.9 

725.3 

802.1 

4.48 

3.48 

5.32 

13.70 

1  .  0336 

791.0 

804.4 

738.7 

788.5 

787.1 

726.3 

792.7 

4.50 

3.32 

5.28 

13.50 

1  .  0337 

775.2 

795.0 

731.9 

779.6 

789.4 

728.4 

784.2 

4.52 

3.22 

4.41 

12.94 

1.0311 

756.8 

756.5 

694.8 

760.0 

791.6 

730.5 

757.9 

4.52 

3.33 

4.82 

13.38 

1.0315 

773.8 

778.7 

715.3 

777.3 

791.6 

730.5 

774.8 

4.52 

3.40 

5.00 

13.35 

1.0313 

767.4 

789  4 

725.0 

776.9 

791.6 

730.5 

783.4 

4.53 

3.56 

5.24 

13.84 

1  .  0334 

798.1 

810.1 

743.0 

798.0 

792.8 

731.6 

799.4 

1926} 


THE  ENERGY  VALUE  OF  MILK 


211 


TABLE  1. — ANALYSES  OP  212  MILK  SAMPLES  WITH  COMPUTED  AND  DETERMINED 
ENERGY  VALUES — (Continued) 


Calories  per  quart 

Fat 

Pro- 

t  ci  11 

Lactose 

Total 

solids 

Specific 

Computed 

gravi  y 

Deter- 
mined 

Meta- 

Form- 

Form- 

Form- 

Form- 

Total 

boliz- 

ula 

ula 

ula 

ula 

A 

B 

C 

D 

E 

F 

able 

1 

2 

3 

4 

perct. 

perct. 

perct. 

perct. 

cals. 

rah. 

4.55 

3.85 

4  92 

13.87 

1.0340 

803.6 

816.2 

744.0 

805.9 

795.0 

733.7 

808.4 

4.55 

3.97 

5.38 

14.69 

1.0355 

845.7 

842.0 

767.8 

837.8 

795.0 

733.7 

827.2 

4.58 

3.80 

4.96 

13.82 

1.0325 

807.3 

816.5 

745.2 

804.5 

798.5 

736.9 

809.5 

4.60 

3.41 

3.91 

12.71 

1  .  0307 

747.7 

754.7 

689.4 

760.0 

800.7 

739.0 

762.1 

4.62 

2.96 

4.60 

13.03 

1.0322 

769.1 

759.1 

701.6 

763.9 

803.0 

741.1 

757.9 

4.63 

3.54 

5.26 

14.06 

1  .  0337 

809.8 

819.1 

752.0 

811.2 

804.1 

742.1 

808.0 

4.64 

3.36 

5.41 

14.18 

1.0331 

812.8 

815.2 

751.3 

812.9 

805.3 

743.2 

803.1 

4.65 

3.80 

4.62 

13.73 

1.0313 

807.8 

808.8 

737.2 

805.7 

806.4 

744.2 

806.8 

4.67 

3.68 

3.64 

12.83 

1  .  0297 

773.0 

764.9 

694.9 

773.3 

807.7 

746.3 

775.9 

4.68 

3.80 

4.69 

14.09 

1.0304 

827.3 

813.5 

741.9 

820.7 

809.8 

747.4 

811.4 

4.74 

4.38 

4.72 

14.74 

1.0344 

858.3 

855.6 

773.9 

858.1 

816.7 

753.7 

849.1 

4.74 

4.04 

5.02 

14.47 

1.0351 

845.8 

848.8 

772.9 

841.5 

816.7 

753.7 

838.7 

4.75 

3.46 

5.42 

14.14 

1.0338 

821.7 

831.7 

765.8 

818.9 

817.8 

754.7 

818.8 

4.76 

4.08 

5.02 

14.41 

1  .  0330 

834.3 

851.1 

774.6 

840.8 

818.9 

755.8 

842.6 

4.82 

3.36 

5.54 

14.42 

1  .  0320 

842.3 

835.6 

771.4 

831.1 

825.7 

762.1 

822.9 

4.87 

3.91 

4.59 

14.19 

1  .  0326 

843.7 

834.6 

760.6 

836.7 

831.4 

767.4 

831.9 

4.88 

3.58 

5.24 

14.06 

1  .  0332 

822.5 

842.6 

774.4 

825.1 

832.6 

768.4 

832.3 

4.88 

3.70 

5.24 

14.20 

1  .  0344 

826.9 

850.4 

780.0 

832.5 

832.6 

768.4 

838.8 

4.88 

4.10 

5.06 

14.66 

1  .  0346 

856.8 

864.9 

788.8 

856.9 

832.6 

768.4 

855.7 

4.94 

3.54 

5.59 

14.58 

1.0348 

842.5 

860.7 

793.0 

846.4 

839.4 

774.8 

844.9 

4.94 

4.12 

4.75 

14.33 

1  .  0340 

842.6 

859.9 

782.2 

848.8 

839.4 

774  8 

853.9 

4.96 

3.23 

5.08 

13.78 

1.0319 

808.7 

823.1 

760.5 

813.4 

841.7 

776.9 

816.2 

4.96 

3.93 

4.88 

14.58 

1.0338 

860.4 

856.1 

781.5 

855.8 

841.7 

776.9 

848.9 

4.97 

3.48 

5.37 

14.30 

1.0329 

836.7 

850.0 

783.3 

837.0 

842.8 

777.9 

838.5 

4.98 

4.26 

5.08 

14.83 

1  .  0358 

874.7 

885.7 

805.6 

871.3 

843.9 

779.0 

874.0 

5.05 

4.09 

4.76 

14.51 

1.0331 

856.4 

867.9 

790.5 

860.8 

851.9 

785.3 

862.5 

5.07 

3.84 

4.79 

14.38 

1  .  0330 

853.9 

856.8 

783.5 

852.8 

854.2 

788.4 

851.6 

5.07 

4.04 

5.09 

14.60 

1.0334 

868.9 

880.7 

804.2 

863.6 

854.2 

788.4 

870.4 

5.10 

4.01 

4.89 

14.76 

1.0337 

872.9 

873.5 

797.3 

871.3 

857.6 

791.6 

866.2 

5.10 

4.02 

4.86 

14.61 

1  .  0328 

871.6 

872.0 

795.8 

865.8 

857.6 

791.6 

865.9 

5.11 

4.02 

4.90 

14.67 

1.0320 

870.0 

873.8 

797.6 

868.5 

858.7 

792.7 

867.9 

5.19 

4.18 

4.82 

14.83 

1  .  0338 

881.8 

888.4 

809.2 

881.7 

867.8 

801.1 

881.7 

5.21 

3.56 

4.96 

14.19 

1.0321 

847.1 

859.6 

790.9 

847.9 

870.1 

803.2 

853.6 

5.21 

3.59 

5.17 

15.04 

1  .  0345 

883.6 

871.4 

802.1 

880.1 

870.1 

803.2 

860.9 

5.21 

4.22 

4.88 

14.89 

1  .  0346 

881.6 

895.5 

815.5 

885.5 

870.1 

803.2 

887.3 

5.22 

3.70 

5.22 

14.65 

1  .  0340 

867.0 

880.0 

808.9 

867.5 

871.2 

804.2 

869.1 

5.22 

4.28 

4.96 

15.10 

1  .  0349 

899.1 

903.1 

822.1 

894.8 

871.2 

804.2 

893.6 

5.23 

3.82 

5.16 

14.64 

1  .  0340 

870.0 

885.3 

812.1 

869.8 

872.4 

805.3 

874.9 

5.23 

4.45 

4.78 

15.16 

1  .  0353 

897.9 

906.9 

822.9 

900.9 

872.4 

805.3 

898.9 

5.25 

3.68 

5.25 

14.72 

1  .  0338 

869.6 

882.6 

811.7 

871.3 

874.7 

807.4 

871.5 

5.27 

3.91 

5.34 

14.90 

1  .  0345 

881.9 

901.3 

826.6 

882.7 

876.  9 

809.5 

888.2 

5.28 

3.66 

4.97 

14.64 

1  .  0329 

880.2 

872.5 

802.0 

870.2 

878.1 

810.6 

865.7 

5.28 

4.07 

5.15 

15.24 

1  .  0352 

901.0 

904.4 

826.8 

899.3 

878.1 

810.6 

892.7 

5.34 

3.45 

5.59 

14.75 

1  .  0346 

879.7 

891.7 

824.6 

872.5 

884.9 

816.9 

876.3 

5.34 

4.13 

4.90 

15.04 

1  .  0350 

905.2 

903.4 

824.5 

896.6 

884.9 

816.9 

894.7 

5.36 

4.24 

4.81 

15.05 

1  .  0337 

898.9 

906.6 

826.0 

900.0 

887.2 

819.0 

900.1 

5.42 

3.95 

5.14 

15.08 

1  .  0360 

902.2 

910.6 

834.7 

898.7 

894.0 

825.3 

898.6 

5.44 

4.06 

5.14 

15.37 

1  .  0358 

921.5 

918.5 

840.6 

912.6 

896.3 

827.4 

906.4 

5.49 

4.78 

4.45 

15.68 

1  .  0356 

950.7 

936.3 

846.1 

940.6 

902.0 

832.7 

931.6 

5.50 

3.71 

5.04 

14.70 

1.0321 

887.3 

897.2 

825.3 

884.7 

903.1 

833.7 

890.2 

5.50 

3.79 

5.00 

14.72 

1  .  0328 

886.2 

900.7 

827.5 

886.9 

903.1 

833.7 

893.5 

5.50 

3.90 

5.08 

15.06 

1  .  0340 

909.0 

911.0 

835.9 

901.4 

903.1 

833.7 

901.6 

5.52 

3.90 

5.07 

15.00 

1  .  0349 

898.7 

913.3 

838.0 

900.3 

905.4 

835.8 

903.1 

5.62 

•3.87 

4.95 

14.98 

1.0337 

902.8 

914.9 

839.9 

904.6 

916.7 

846.3 

907.3 

5.62 

4.21 

4.84 

15.30 

1  .  0359 

913.8 

931.6 

850.7 

922.7 

916.7 

846.3 

922.9 

5.66 

3.62 

5.25 

15.02 

1.0326 

909.0 

915.2 

844.5 

903.2 

921.2 

850  6 

905.4 

5.66 

4.21 

5.14 

15.59 

1  .  0355 

951.9 

946.4 

865.7 

935.0 

921.2 

850.6 

934.5 

5.72 

3.83 

5.20 

15.28 

1.0351 

927.4 

932.6 

858.1 

920.0 

928.1 

856.9 

920.9 

5.76 

3.52 

4.84 

14.98 

1  .  0336 

916.8 

903.6 

834.2 

906.5 

932.7 

861.1 

898.1 

5.76 

4.08 

5.33 

15.57 

1  .  0367 

924.0 

956.8 

877.9 

936.9 

932.7 

861.1 

941.6 

5.79 

4  00 

5.18 

15.47 

1  .  0342 

928.5 

946.8 

869.4 

933.7 

936.1 

864.2 

936.0 

5.86 

3.73 

4.96 

15.04 

1  .  0328 

911.0 

928.3 

855.2 

917.2 

944.0 

871.6 

921.8 

5.87 

4.19 

4.90 

15.70 

1  .  0339 

951.9 

953.6 

872.7 

950.5 

945.2 

872.7 

946.0 

5.88 

3.84 

4.97 

15.61 

]  .  0323 

944.7 

936.2 

861.3 

941.6 

946.3 

873.7 

929.8 

5.88 

4.10 

4.94 

15.54 

1  .  0357 

940.8 

952.7 

873.1 

943.4 

946.3 

873.7 

943.1 

5.90 

3.98 

5.34 

15.86 

1.0361 

957.7 

963.7 

886.2 

953.6 

948.6 

875.8 

949.1 

5.94 

4.26 

5.26 

16.03 

1  .  0355 

963  6 

979.3 

897.0 

966.9 

953  1 

SSI  1.0 

9I>5.S 

212 


BULLETIN  No.  282 


[December, 


TABLE  1. — ANALYSES  OF  212  MILK  SAMPLES  WITH  COMPUTED  AND  DETERMINED 
ENERGY  VALUES — (Concluded) 


Calories  per  quart 

Fat 

Pro- 

Lactose 

Total 

Specific 

Computed 

Deter- 
mined 

Meta- 

Form- 

Form- 

Form- 

Form- 

Total 

boliz- 

ula 

ula 

ula 

ula 

A 

B 

C 

D 

E 

F 

able 

1 

2 

3 

4 

perct. 

perct. 

perct. 

perct. 

cals. 

cals. 

5.94 

4.32 

5.00 

15.97 

1.0342 

964.2 

971.3 

888.1 

966.3 

953.1 

880.0 

962.1 

5.96 

4.05 

4.66 

15.33 

1.0336 

950.2 

944.3 

865.5 

939.5 

955.4 

882.1 

940.2 

5.98 

3.88 

4.90 

15.43 

1  .  0342 

937.0 

946.5 

870.5 

941.0 

957.8 

884.3 

939.2 

5.99 

4.12 

5.26 

15.98 

1.0353 

962.6 

975.7 

895.8 

965.3 

958.8 

885.3 

962.7 

6.00 

3.69 

5.18 

15.33 

1.0323 

935.0 

946.7 

874.2 

934.3 

960.0 

886.4 

938.2 

6.04 

4.31 

5.14 

16.08 

1.0349 

981.0 

985.9 

902.6 

975.2 

964.5 

890.6 

974.4 

6.05 

4.83 

4.14 

15.87 

1  .  0352 

988.7 

977.4 

884.9 

979.1 

965.6 

891.6 

976.8 

6.16 

3.69 

4.86 

15.16 

1.0326 

939.7 

949.1 

876.0 

937.2 

978.2 

903.2 

944.1 

6.42 

3.95 

5.24 

16.27 

1.0351 

992.7 

1004.2 

926.1 

996.3 

1007.7 

903.6 

992.0 

6.56 

4.34 

5.02 

16.58 

1  .  0338 

1020.2 

1028.8 

943.9 

1022.3 

1023.6 

945.3 

1020.0 

7.59 

3.23 

5.00 

16.69 

1.0314 

1070.7 

1056.6 

988.1 

1062.6 

1140.8 

1053  .  8 

1052.6 

STATISTICAL  PARTa 

The  total  computed  calories  per  quart  for  each  of  the  212  samples 
tabulated  in  Table  1,  were  obtained  with  a  computing  machine  by  com- 
pleting the  following  computations:  total  calories  per  quart  =  (A  X  9.23 
+  B  X  5.71  +  C  X  3.95)  (946.36  X  E)  •*•  100.  In  this  expression  the 
values  9.23,  5.71,  and  3.955  are  large  calories  of  heat  evolved  by  the 
complete  combustion  of  one  gram  of  butterfat,  one  gram  of  protein, 
and  one  gram  of  lactose,  respectively;  946.36  is  the  volume  of  one  quart 
in  milliliters. 

The  metabolizable  calories  per  quart  given  in  the  eighth  column  in 
Table  1  were  obtained  by  completing  the  indicated  computation: 
[A  X  9.00  +  (B  +  C)  4.00]  [946.36  X  E]  -4-  100.  In  this  expression  the 
values6  9.00  and  4.00  are  the  metabolizable  energy  values,  in  large 
calories,  of  one  gram  of  butterfat  and  one  gram  of  protein  and  carbo- 
hydrate, respectively. 

The  means,  standard  deviations,  coefficients  of  correlations,  and 
partial  regression  coefficients  of  the  analytical  results  in  columns  A  to  F 
inclusive  are  given  in  Table  2.  The  partial  regression  coefficients  were 
computed  by  the  method  given  by  Wallace  and  Snedecor.7 

From  the  results  given  in  Table  2,  regression  equations  were  de- 
veloped by  substitution  in  the  general  regression  equations.  The  re- 


aln  the  statistical  part,  the  following  symbols  are  used: 

A  =  percentage  of  fat  in  the  sample. 

B  =  percentage  of  protein  in  the  sample. 

C  =  percentage  of  sugar  (lactose)  in  the  sample. 

D  =  percentage  of  total  solids  in  the  sample. 

E  =  specific  gravity  of  the  sample  at  20°C. 

F  =  determined  calories  per  quart. 

Fu  —  computed  calories  per  quart  (metabolizable). 

FT  =  computed  calories  per  quart  (total). 


1926] 


THE  ENERGY  VALUE  OF  MILK 


213 


gression  equation  of  F,  based  upon  the  other  variables,  is  F  =  MF  + 
aF  aF  aF  aF 

(D  —  MD)  +  @FE  .   ~^  (E  —  ME).      Substituting  the  values  given  in 
Table  2,  and  simplifying,  this  equation  becomes, 

F!  =  52.78A  +  16.415  +  37.87D  +  46.91E  -  2.75C  -  57.70 
calories  per  quart  (Formula  1). 


TABLE  2. — MEANS,  STANDARD  DEVIATIONS,  COEFFICIENTS  OF  CORRELATIONS  AND 

PARTIAL  REGRESSION  COEFFICIENTS  DERIVED  FROM  ANALYSES  OF 

212  MILK  SAMPLES  SHOWN  IN  TABLE  1 


Column 

Means 

Standard  deviations 

Coefficients  of 
correlations 

A 
B 
C 
D 
E 
F 

F 
1  it 

4.2717  ±  .0452 
3.4620  +  .0211 
4.9519  +  .0140 
13.3000  ±  .0663 
1  .0328  ±  .00007 
763.02  ±5.17 
704.386  ±4.839 

.9761  +  .0320 
.4558  +  .0149 
.3021  ±  .0099 
1.4316  ±  .0469 
.0015  +  .00005 
111.681  +  3.658 
104.463  +3.422 

rAB  =  .7923  ±  .0172 
rAC  =  .1837  +  .0448 
rAD  =  .9640  ±  .0033 
rAE=  .5657  ±  .0315 
rAV  =  .9813  ±  .0017 
rBC  =  .0426  +  .0462 
rBD  =  .8653  ±  .0116 

r».  =  .6842  ±  .0246 
r_.  =  .8525  ±  .0127 
rcl)  =  .3025  ±  .0421 
rCE  =  .4687  +  .0361 
rcf  =  .2274  +  .0439 
rDB  =  .6965  ±  .0238 

rD.  =  .9862  ±  .0013 
rEF  =  .6419  ±  .0272 
rAF    =  .9838  ±  .0015 

•y 

(/3  for  six  variables) 
0fA  =  .46132 
£„  =  .06696 
|8,c  =  .00745 
£„  =  .48542 
PfK  =  .00063 
(0  for  variables  A,  B,  C,  and  F 
e,A  =  .7925 
0M  =  .2215 
Prc  =  -0723 

The  regression  equation81  of  F  on  A  is  F  =  MF  + 
MA)  ;  which  becomes, 


aF 


=  113.7334  (A  +  2.4404)  calories  per  quart  (Formula  2). 


"As  the  regression  equation  of  F  on  A  is  most  likely  to  be  of  practical  value,  it 
was  determined,  without  grouping,  from  the  data  given  in  columns  A  and  F,  Tible  1, 
by  the  method  set  forth  by  Wallace  and  Snedecor.7  The  means,  the  standard 
deviations,  and  the  coefficient  of  correlation  are  as  follows:  MA  =  4.2686,  MF  = 
763.036,  aA  =  .969632,  a,  =  111.7665,  rAr  =  .9867. 

It  is  interesting  to  observe  that  the  regression  equation  of  F  on  A,  based  en  the 
statistical  values  obtained  by  grouping  the  data  into  classes  given  in  Table  2,  is 
Fz  =  112.276  (A  +  2.524).  In  this  case  the  slope  of  the  line  constructed  by  plotting 
the  estimated  F's  against  their  corresponding  percentages  of  fat  is  less  than  the  slope 
of  the  line  obtained  when  the  equation  derived  without  grouping  into  classes  is  used. 
The  other  regression  equations  are  derived  from  the  statistical  values  obtainei  by 
grouping  the  data. 


214  BULLETIN  No.  282  [December, 

The  correlation  coefficient  of  A  and  FM,  the  metabolizable  energy 
value  (Table  1,  eighth  column),  was  computed.  The  regression  equation 
in  this  case  becomes, 

7^3  =  105.287  (A  +  2.4185)  calories  per  quart  (metabolizable) 

(Formula  3). 

The  regression  equation  for  F,  based  on  A,  B,  and  C,  computed 
from  the  data  given  in  Table  2,  becomes, 

7^4  =  90.67A  +  54.275  +  26.73C  +  55.44  calories  per  quart 

(Formula  4). 

These  formulas  may  be  used  for  estimating  the  energy  value  of 
a  quart  of  milk.  The  values  of  the  212  samples  used  in  this  investiga- 
tion, ranging  in  fat  percentage  from  2.68  to  7.59,  so  computed,  are  in- 
cluded in  Table  1  in  the  columns  headed  by  the  respective  formula 
numbers. 

The  multiple  correlation  coefficients  may  be  computed  by  substi- 
tuting the  values  from  Table  2  in  the  equation,7  R2  =  j3FA  •  rAF  -f  $FB  - 
fsf  +  (etc.).  In  the  case  of  the  six  variables  this  becomes  R\  —  \/-98726 
=  .9936;  and  for  the  four  variables,  A,  B,  C,  and  F,  it  becomes  R2  — 
V.9830  =  .9915. 

)  The  standard  error  of  estimate  in  the  energy  values  computed  by 
the  use  of  Formula  1  is  cF  -  ABCDE  =  aF  \/l  -  R?  =  cF  \/l  -  .98726 
=  .1128  <sF,  or  11.28  percent  of  the  standard  deviation  of  F.  In  the  case 
of  Formula  4  the  standard  error  of  estimate  is  aF  •  ABC  =  <sF  \/l  —  R^ 
=  cF  Vl  -  ,9830  =  .1304,  or  13.04  percent  of  the  standard  devi- 
atior  of  F. 

For  Formulas  2a  and  3  the"  standard  errors  of  estimate  are,  re- 


spectively, cF  •  A  =aF  Vl  -  I*AF  =  °F  Vl  -  (.9867)2  =  .1626  oF, 
or  16.26  percent  of  the  standard  deviation  of  F,  and  <sFM  •  A  =  aFM 


-  (.9838)2  =  .1793  aFM,  or  17.93  percent  of  the 
standard  deviation  of  FM- 

The  differences  were  found  between  the  determined  energy  values 
(Cohmn  F,  Table  1)  and  the  total  computed  values  given  in  the  columns 
heaced  Total,  Formula  1,  Formula  2,  and  Formula  4,  respectively; 
and  also  between  the  computed  metabolizable  energy  and  Formula  3. 
The  means,  standard  deviations,  and  limits  at  odds  of  30:1  and  at  odds 
of  100:1  for  these  five  sets  of  differences  are  given  in  Table  3. 


"Using  for  Formula  2  the  statistical  values  given  in  the  preceding  footnote, 
pags  213. 


1926} 


THE  ENERGY  VALUE  OF  MILK 


215 


APPLICATION 

The  regression  equations  give  a  convenient  method  for  use  in  com- 
puting the  energy  value  of  a  quart  of  milk  if  the  percentage  composition 
of  the  milk  is  known.  If  A,  B,  C,  D,  and  E  are  known,  Formula  1  may 
be  used.  When  A,  B,  and  C  are  known,  Formula  4  is  to  be  used,  and 
Formula  2  when  A  only  is  known.  To  compute  the  metabolizable 
energy  value  of  a  quart  of  milk  when  A  only  is  known,  Formula  3  is  to 
be  used. 

Table  3,  giving  means,  standard  deviations,  and  limits  within  which 
the  results  computed  by  the  various  formulas  will  lie,  gives  a  measure 
of  the  reliability  of  the  computed  values. 

TABLE  3. — MEANS  AND  STANDARD  DEVIATIONS  OP  THE  DIFFERENCES  AND  LIMITS 


Differ- 
ences 

Number 

of  differ- 
ences 

Mean 

Standard 
deviation 

Limits  at 
odds  of 
30:1 

Limits  at 
odds  of 
100:1 

cals. 

cals. 

cals. 

cals. 

Fl-F* 
F2l-F** 

F*T-F 

212 
212 
212 
212 
212 
212 

+  .1416 
-.0071 
-  .4437 
-.4436 
-  .3702 
+6.3584 

5.7081  +  .1870 
18.1755  ±  .5953 
18.2448  +  .5976 
14.9076  +  .4882 
8.3356  +  .2730 
8.5812  +  .2811 

±  12.2153 
±  38.9056 
+  39.0439 
±  31.9023 
±  17.8382 
±  18.3638 

±  14.7269 
±  46.8928 
+  47.0267 
+  38.4616 
+  21.5058 
±  22.1395 

F  =  calories  per  quart,  determined.                            Fa  =  calories   per   quart,   computed   by  Form- 

F2l 


calories   per   quart,   computed  by   Form- 
ula 1. 

calories   per  quart,   computed   by   Form- 
ula 2. 

=  calories  per  quart,  computed  from  re- 
gression equation  obtained  from  grouped 
data. 


ula  3. 

Ft  =  calories  per  quart,  computed  by  Form- 
ula 4. 

FM  =  calories  per  quart  metabolizable. 

FT  :=  calories  per  quart,  computed  from  energy 
value  of  constituents. 


*The  mean  and  the  standard  deviation  of  the  differences  Fz  —  F  were  determined 
without  grouping  the  data  into  classes;  all  other  means  and  standard  deviations  in 
this  table  were  determined  from  grouped  data. 

**The  values  FZl  were  obtained  by  the  use  of  the  regression  equation  given  in  the 
footnote  on  page  213.  The  standard  deviations  and  limits  for  F2  —  F  and  for  F2j  —  F 
show  that  the  results  obtained  by  grouping  are  only  slightly  different  from  those 
obtained  without  grouping. 


Formula  1  gives  results  which  at  odds  of  30:1*  will  lie  within 
+  12.2153  calories  per  quart  of  the  determined  value.  These  limits 
are  within  about  +  2  percent  of  the  determined  values  for  milk  with 
low  fat  content,  and  within  +1.25  percent  for  milk  with  high  fat 
content. 


•The  mean  of  each  group  of  differences  ±  2.14  times  the  corresponding  standard 
deviation  gives  limits  such  that  the  chances  are  30:1  that  any  single  difference  de- 
termined in  the  same  way  will  fall  within  them.  For  odds  of  100:1  the  standard  devi- 
ation is  to  be  multiplied  by  ±  2.58. 

The  constants  +  2.14  and  ±  2.58  were  determined  from  the  equation  given  on 
page  28  of  Karl  Pearson's  Tables  for  Statisticians  and  Biometricians. 


216  BULLETIN  No.  282  [December, 

Formula  2  gives  results  which  at  odds  of  30:1  will  lie  within  ± 
38.8956  calories  per  quart  of  the  determined  value,  or  within  about 
+  6.5  percent  for  milk  with  low  fat  content,  and  ±  3.9  percent  for  milk 
with  high  fat  content. 

Formula  3  gives  values  which  at  odds  of  30:1  will  lie  within  ± 
31.9023  calories  per  quart  of  the  computed  metabolizable  energy  value, 
or  within  about  +  6  percent  of  the  computed  value  for  milk  with  low 
fat  content,  and  ±  3.4  percent  for  milk  with  high  fat  content. 

Formula  4  gives  values  which  at  odds  of  30:1  will  lie  within  ± 
17.8382  calories  per  quart  of  the  determined  value,  or  within  about 
+  3.4  percent  for  milk  with  low  fat  content,  and  +  2  percent  for  milk 
with  high  fat  content. 

The  mean  and  standard  deviation  of  the  differences  between  the 
total  energy  per  quart  as  computed  and  as  determined  show  that  for 
the  values  for  fat,  for  protein,  and  for  lactose,  as  used  in  this  work,  the 
computed  values  are,  on  the  average,  6.3584  calories  per  quart  higher 
than  the  determined  values.  They  also  show  that  if  6.3584  calories  are 
substracted  from  the  computed  values,  the  chances  are  30:1  that  such 
values  will  then  lie  within  +  18.3638  calories  per  quart  of  the  deter- 
mined values.a 

The  standard  errors  of  estimate  show  that  the  standard  deviations 
of  computed  values  from  determined  values  are,  for  Formula  1,  11.28 
percent  of  the  standard  deviation  of  F;  for  Formulas  2  and  4,  16.26 
percent  and  13.04  percent,  respectively,  of  the  standard  deviation  of  F; 
and  for  Formula  3  the  standard  deviation  of  values  computed  by  the 
formula,  from  those  obtained  by  the  use  of  the  metabolizable  energy 
value  of  the  constituents  (FM),  is  17.93  percent  of  the  standard  devia- 
tion of  FM> 

For  the  purpose  of  comparing  results  obtained  by  their  use,  with 
results  obtained  by  using  Formula  2  of  this  work,  the  formulas  of  Gaines 
and  Davidson  and  of  Andersen  were  changed  to  the  basis  of  the  average 
weight  of  a  quart  of  milk  (977.4  grams).  These  formulas  thus  become, 
E  =  106.9643  (2.66  +  t)  calories  per  quart,  and  E  =  110.9349  (per- 
centage of  fat  +  2.555)  calories  per  quart,  respectively. 


•If  the  values  given  by  Frederiksen  asfound  by  Andersen3  (butterfat,  9.11  calories 
per  gram;  milk  protein,  5.86  calories;  and  lactose,  3.76  calories  per  gram)  are  used, 
the  results  are  as  follows:  mean  of  the  differences  between  the  determined  energy 
value  per  quart  and  the  value  computed  by  Andersen's  constants,  —  2.8302  calories; 
standard  deviation  of  these  differences,  8.5485  calories.  That  is,  the  energy  of  a 
quart  of  milk  computed  in  this  way  is  on  the  average  2.8302  calories  less  than  the 
determined  energy.  At  odds  of  30:1,  the  limits  within  which  computed  values  may  be 
expected  to  fall  are  +  18.2938;  and  at  odds  of  100:1,  the  limits  are  ±  22.0551.  This 
work  of  Andersen's  was  not  at  hand  when  the  statistical  study  shown  in  the  tables 
was  made. 


1926} 


THE  ENERGY  VALUE  OF  MILK 


217 


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750 

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440 

430 

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Mea.n  determined 
i/a-lue 

Values  computed 
from  formula.    2 

Valuta  computed 
from  Andersen's  form. 
Values,  computed 
'rom  Ga-ines'  a.nd 
Da-vidson's  forjnulaL 

£ 

>// 

/ 

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2 

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1.80    3.1O      3.+0     3.70     -J-OO    4-.3O    4.tO    +.30    J.2O     55O     5.60    4.1O      M-0 

Percent  a.£es  of  Ta.t 


7.30    7.40 


DETERMINED  AND  COMPUTED  ENERGY  VALUES  OF  MILK 

The  energy  value  of  milk  of  a  given  fat  content,  computed  by  formula,  corre- 
sponds very  closely  to  the  value  determined  in  the  calorimeter. 


The  results  as  computed  by  each  formula  are  compared  graphically 
with  each  other  and  with  the  mean  determined  results  in  the  accom- 
panying figure.  These  graphs  show  that  the  energy  values  computed 
by  the  formulas  correspond  very  closely  with  the  determined  values 


218  BULLETIN  No.  282 

CONCLUSIONS 

1.  The  heat  of  combustion  of  a  quart  of  milk  may  be  computed 
in  one  of  the  following  ways: 

a.  If  the  percentages  of  fat,  protein,  lactose  and  total  solids,  and 
the  specific  gravity  are  known,    the  formula  F  =  52.78A  +  16.411?  -f- 
37.87D  +  46.9 IE  -  2.75C  -  57.70  should  be  used. 

b.  If  the  percentages  of  fat,  protein,  and  lactose  are  known,  the 
formula  F  =  90.67A  +  54.275  +  26.73(7  +  55.44  should  be  used. 

c.  If  only  the  percentage  of  fat  is  known,  the  formula  F  =  113.7334 
(A  +  2.4404)  should  be  used. 

d.  If  only  the  percentage  of  fat  is  known  and  the  metabolizable 
energy  is  wanted,  the  formula  FM  =  105.287  (A  +  2.4185)  should  be 
used. 

2.  The  true  heats  of  combustion  per  gram  of  butterfat,  milk  pro- 
tein, and  lactose  probably  lie  between  the  values  given  by  Abderhalden5 
and  by  Hammarsten5  and  those  given  by  Frederiksen  as  found  by 
Andersen.3 

LITERATURE  CITED 

1.  GAINES,  W.  L.,  AND  DAVIDSON,  F.  A. 

Relation  between  percentage  fat  content  and  yield  of  milk.  111. 
Agr.  Exp.  Sta.  Bui.  245.  1923. 

2.  STOCKING,  W.  A.,  AND  BREW,  J.  D. 

Milk,  the  essential  food.   Dairymen's  League  News.  Jan.  10,  1920. 

3.  iFREDERIKSEN,   LARS. 

Second  Communication  from  the  Experiment  Station,  Div.  of 
Anim.  Husb.,  Roy.  Vet.  and  Agr.  Col.  Copenhagen,  Denmark. 
1925. 

4.  PALMER,  L.  S. 

The  preservation  of  milk  for  chemical  analysis.  Mo.  Agr.  Exp.  Sta. 
Res.  Bui.  34,  29.  1919. 

5.  ABDERHALDEN,  EMIL. 

Text-book  of  physiological  chemistry,  1st  ed.,  333.    1908. 
HAMMARSTEN-MANDEL.  Text-book  of  physiological  chemistry, 
6th  ed.,  829.   1912. 

6.  SHERMAN,  H.  C. 

Chemistry  of  food  and  nutrition.    3d  ed.    1926. 

7.  WALLACE,  H.  W.,  AND  SNEDECOR,  GEORGE  W. 

Correlation  and  machine  calculation.  la.  State  Col.  of  Agr.  and 
Mech.  Arts.  Official  Publication  23,  No.  35,  28-33.  1925. 


UNIVERSITY  OF  ILLINOIS-URBANA 


